Disclaimer
This calculator is for educational and curiosity purposes only. No gaurantee on accuracy is inferred by a result.
Calculation Process
This approximation for a first cell height follows the process as outlined in several references regarding turbulence modeling. The process is well established and starts with the assumption that a desired value of y+ is known. This is typically based on the turbulence model being used in your numerical approach. The process is as follows.
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Calculate the Reynolds number for the flow field using the length of the boundary layer as the characteristic length term.
\[Re = \frac{\rho V l}{\mu}\]
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Estimate the skin friction coefficient using one of the available models.
Schlichting: \(C_f = {[2\log_{10}(Re_x)-0.65]^{-2.3}}\) for \(Re_x < 10^9\)
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Calculate wall shear stress based on the result from above.
\[\tau_w = C_f \: q_\infty \]where \(q_\infty\) is the dynamic pressure and is given by \[q_\infty = {1 \over 2} \rho V^2\]
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Calculate the friction velocity.
\[u_* = \sqrt{\frac{\tau_w}{\rho}}\]
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Calculate the dimensional wall distance.
\[y = \frac{y^+ \mu}{\rho \: u_*}\]